\section{Features}

We tried a variety of features, but ultimately settled on eight. \textbf{MAX HEIGHT} and \textbf{MIN HEIGHT} computed the heights of the tallest and shortest columns respectively. Both features encouraged keeping the heights of the columns even. \textbf{NUM SQUARES} counted the number of occupied cells on the board. \textbf{LINES CLEARED} counted the number of lines cleared by dropping a given piece. Both \textbf{NUM SQUARES} and \textbf{LINES CLEARED} capture the elimination of pieces from the board. We had two features on gaps in the board: \textbf{OVERHANGS} computed the number of empty cells covered by at least one occupied cell and \textbf{holes} counted the number of empty cells with occupied cells both above and below. \textbf{DIFFS} captured the jaggedness of the board by summing the absolute differences in heights of adjacent columns. \textbf{ISOLATION} was a measure of horizontal separation: it summed the number of horizontally adjacent empty cells across all occupied cells.

%As mention in the cross entropy results, \textbf{ISOLATION} and \textbf{OVERHANGS} were particularly important features for us. The height related features, like \textbf{MAX HEIGHT}, \textbf{MIN HEIGHT} and\textbf{DIFFS} were less important. We could remove them without a huge loss in performance.

Other features we considered but did not use include \textbf{SUM HEIGHT} which would compute the sum of all column heights and \textbf{WELLS} which would compute the depths of wells of empty spaces. We avoided \textbf{SUM HEIGHT} because, like the rest of height-related features, it did not improve performance much. Further, it was highly correlated with \textbf{MAX HEIGHT} and \textbf{MIN HEIGHT}. \textbf{WELLS} was designed to penalize columns of empty space that could only be filled by long, skinny pieces. Surprisingly, its inclusion hurt performance.